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 A266805 Coefficient of x in the minimal polynomial of the continued fraction [1^n,sqrt(6),1,1,...], where 1^n means n ones. 5
 -14, -90, -722, -4830, -33554, -228954, -1572110, -10768122, -73825010, -505954014, -3467991794, -23769625530, -162920337422, -1116670248090, -7653777913874, -52459758093534, -359564573392850, -2464492138756122, -16891880703949070, -115778671987640634 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A265762 for a guide to related sequences. LINKS Index entries for linear recurrences with constant coefficients, signature (5,15,-15,-5,1). FORMULA a(n) = 5*a(n-1) + 15*a(n-2) - 15*a(n-3) - 5*a(n-4) + a(n-5) . G.f.:  -((2 (-7 - 10 x - 31 x^2 - 40 x^3 + 3 x^4))/(-1 + 5 x + 15 x^2 - 15 x^3 - 5 x^4 + x^5)). EXAMPLE Let p(n,x) be the minimal polynomial of the number given by the n-th continued fraction: [sqrt(6),1,1,1,...] has p(0,x) = 19-14x-13x^2+2x^3+x^4, so a(0) = -14; [1,sqrt(6),1,1,1,...] has p(1,x) = 19-90x+143x^2-90x^3+19x^4, so a(1) = -90; [1,1,sqrt(6),1,1,1...] has p(2,x) = 361-722x+527x^2-166x^3+19x^4, so a(2) = -722. MATHEMATICA u[n_] := Table[1, {k, 1, n}]; t[n_] := Join[u[n], {Sqrt[6]}, {{1}}]; f[n_] := FromContinuedFraction[t[n]]; t = Table[MinimalPolynomial[f[n], x], {n, 0, 40}]; Coefficient[t, x, 0] ; (* A266804 *) Coefficient[t, x, 1];  (* A266805 *) Coefficient[t, x, 2];  (* A266806 *) Coefficient[t, x, 3];  (* A266807 *) Coefficient[t, x, 4];  (* A266804 *) CROSSREFS Cf. A265762, A266804, A266806, A266807. Sequence in context: A114242 A054487 A200191 * A301380 A047639 A202291 Adjacent sequences:  A266802 A266803 A266804 * A266806 A266807 A266808 KEYWORD easy,sign AUTHOR Clark Kimberling, Jan 09 2016 STATUS approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)